What is the probability that she lost no money?

A tourist in Las Vegas was attracted by a certain gambling game in which the customer stakes $1$ dollar on each play; a win then pays the customer $2$ dollars plus the return of her stake, although a loss costs her only her stake. Las Vegas insiders, and alert students of probability theory, know that the probability of winning at this game is $\frac{1}{4}$. When driven from the tables by hunger, the tourist had played this game $240$ times. What is the probability that she lost no money?

For this, I found $E(X)=.25$, then I multiplied the $E(X)$ by $240$ to get $60$. Afterwards, I knew I needed to find $V(X)$, so I got $\frac{9}{4}$ as my variance, then I got the standard deviation and tried to find the area of the normal distribution when $X>0$, but couldn't solve it.

• What standard deviation did you get? How did you try to apply that knowledge to the area of a normal distribution? – David K Oct 23 '17 at 19:04
• The expectation is negative, not positive. – Ross Millikan Oct 23 '17 at 19:20